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# In the correctly worked addition problem shown, where the

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Joined: 10 Apr 2018
Posts: 268
Location: United States (NC)

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03 Apr 2019, 14:00
Hi, here are my two cents for this question

AB+BA = AAC

this means that B+A = X ( Say )

Now if we add any two digits the carry forward to tens digit can be either 0 or 1

If there was no carryforward from addition then X =C, if there was carry forward from addition then X=1C

Because in tens digit of addition A+B = AA, this means that carry forward from ones place was 1. if there was no carry forward from ones place then tens place would also be C .

this means in units digit the addition of B+A leads us to 1C, where C is in the units place of sum and 1 is taken as carry forward from addition.

So A+B= X= which is two digit number starting with 1_

so we know from ones place addition that B+A = 1C

so in tens place of addition we have A+B+1=AA

1C+1= AA
so 1C+1= 10A+A
1C+1= 11A
1C= 11A-1
1C= 11A-1
For any other value of A except 1 the value of C wouldn't have ten's place as 1. eg A= 2, C= 21, A=3 C=32
So A=1 now that means 1C=10
hence C =0

Now if A=1 , we have B= 9

AB+BA=
In Ones place we have B+A= 1+9=10, so 0 remains in units place of addition and 1 goes as carry forward.

In Tens place of addition we have A+B+1= 1+9+1= 11
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Probus

~You Just Can't beat the person who never gives up~ Babe Ruth
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Joined: 30 Dec 2018
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26 May 2019, 00:17
AB
+BA
=AAC

11*A+11*B=101*A+C
11*(B-9A)=C
as C is a positive integer in [0,9] B-9A=0
B=9A
A cannot be 0 because A, B cannot be the same number and A, B both are +ve integers from 0 to 9
If A>= 2 B is a two digit number therefore not possible for A in [2,9]
therefore A=1 ,B=9,C=0
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Joined: 17 May 2019
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05 Jul 2019, 20:03
Spunkerspawn wrote:
My solution was a bit lengthy but it worked:

AB + BA = AAC
10A + B + 10B + A = 100A + 10A + C (cancel out the 10A's)
B + 10B + A - 100A = C
B(1+10) + A(1 - 100) = C

11B - 99A = C

the only value for C that satisfies this equation is C = 0. Then B = 9 and A = 1

How can we know that 0 is the only value to satify the equation ? Followed a similar approach but got stuck
Re: In the correctly worked addition problem shown, where the   [#permalink] 05 Jul 2019, 20:03

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